In [1]} it is also claimed that the index structure used for quantifier
elimination can be updated in constant time. It then tempting to think that
enumeration could be achieved by adding each newly derived output tuple to the index
structure and obtain the next output in constant time using the updated index.
This idea does not work because constant update time can only be achieved if
the inserted tuple does not modify too much the structure of the underlying graph. In
particular the new structure must stay within the class under
investigation. This is typically not the case with first-order query that may
produce very dense results.
